Conventionally, there has been known an oxygen sensor which is disposed in an exhaust pipe of an internal combustion engine of a vehicle and which responses the concentration of oxygen contained in exhaust gas and detects the air-fuel ratio of the internal combustion engine (i.e., whether the air-fuel ratio is in a rich state or a lean state). The detection element of this oxygen sensor is mainly formed of a solid electrolyte body such as zirconia, and its output voltage (sensor output) corresponding to the air-fuel ratio of the internal combustion engine sharply changes, like a binary value, at the stoichiometric air-fuel ratio. Therefore, by utilizing this phenomenon, it is possible to determine whether the air-fuel ratio of fuel mixture burned in the internal combustion engine is on the rich side or the lean side. Notably, the solid electrolyte body which forms the detection element exhibits sufficiently high oxygen ion conductivity at a high temperature of about 600° C. or higher (active state). Therefore, a heater for heating the detection element is provided in the oxygen sensor so as to heat the detection element to thereby bring the detection element in an active state. Further, by making use of the phenomenon that the element impedance (internal resistance) of the detection element changes in accordance with the element temperature, the supply of electricity to the heater is feedback-controlled such that the element impedance (internal resistance) becomes equal to a target impedance (target resistance) whereby the detection element is maintained at a predetermined temperature within a range in which the detection element is activated. For example, Patent Document 1 discloses an oxygen concentration detection apparatus for an oxygen sensor having a detection element and a heater, which detection apparatus controls the temperature of the detection element by feedback-controlling the power supplied to the heater.